198
个编辑
更改
跳到导航
跳到搜索
第557行：
第557行： + + + + + + + + + + + + + + + + + + + + + + + 第572行：
第595行： + + + + + + + + + + +
→适应度模型
=== 适应度模型 ===
=== 适应度模型 ===
Another model where the key ingredient is the nature of the vertex has been introduced by Caldarelli et al.<ref>Caldarelli G., A. Capocci, P. De Los Rios, M.A. Muñoz, Physical Review Letters 89, 258702 (2002)</ref> Here a link is created between two vertices <math>i,j</math> with a probability given by a linking function <math>f(\eta_i,\eta_j)</math> of the [[Fitness model (network theory)|fitnesses]] of the vertices involved.
Caldarelli等人引入了另一个模型，其中关键成分是顶点的性质。<ref>Caldarelli G., A. Capocci, P. De Los Rios, M.A. Muñoz, Physical Review Letters 89, 258702 (2002)</ref> 两个顶点<math>i,j</math>之间的连接概率由连接函数<math>f(\eta_i,\eta_j)</math> 给出，该函数是网络节点[[适应性模型（图论）|适应性]]的函数。
Caldarelli等人引入了另一个模型，其中关键成分是顶点的性质。<ref>Caldarelli G., A. Capocci, P. De Los Rios, M.A. Muñoz, Physical Review Letters 89, 258702 (2002)</ref> 两个顶点<math>i,j</math>之间的连接概率由连接函数<math>f(\eta_i,\eta_j)</math> 给出，该函数是网络节点[[适应性模型（图论）|适应性]]的函数。
The degree of a vertex i is given by <ref>Servedio V.D.P., G. Caldarelli, P. Buttà, Physical Review E 70, 056126 (2004)</ref>
:<math>k(\eta_i)=N\int_0^\infty f(\eta_i,\eta_j) \rho(\eta_j) \, d\eta_j </math>
节点的度由下式给出<ref>Servedio V.D.P., G. Caldarelli, P. Buttà, Physical Review E 70, 056126 (2004)</ref>
节点的度由下式给出<ref>Servedio V.D.P., G. Caldarelli, P. Buttà, Physical Review E 70, 056126 (2004)</ref>
:<math>k(\eta_i)=N\int_0^\infty f(\eta_i,\eta_j) \rho(\eta_j) \, d\eta_j </math>
:<math>k(\eta_i)=N\int_0^\infty f(\eta_i,\eta_j) \rho(\eta_j) \, d\eta_j </math>
If <math>k(\eta_i)</math> is an invertible and increasing function of <math>\eta_i</math>, then
the probability distribution <math>P(k)</math> is given by
:<math>P(k)=\rho(\eta(k)) \cdot \eta'(k)</math>
如果<math>k(\eta_i)</math>是<math>\eta_i</math>的可逆递增函数，那么<math>P(k)</math>的概率分布为
如果<math>k(\eta_i)</math>是<math>\eta_i</math>的可逆递增函数，那么<math>P(k)</math>的概率分布为
:<math>P(k)=\rho(\eta(k)) \cdot \eta'(k)</math>
:<math>P(k)=\rho(\eta(k)) \cdot \eta'(k)</math>
As a result, if the fitnesses <math>\eta</math> are distributed as a power law, then also the node degree does.
因此，如果适应性<math>\eta</math>是幂律分布，那么节点的度遵循幂律分布。
因此，如果适应性<math>\eta</math>是幂律分布，那么节点的度遵循幂律分布。
Less intuitively with a fast decaying probability distribution as
<math>\rho(\eta)=e^{-\eta}</math> together with a linking function of the kind
:<math> f(\eta_i,\eta_j)=\Theta(\eta_i+\eta_j-Z)</math>
不那么直观地，一个快速衰减的概率分布函数
不那么直观地，一个快速衰减的概率分布函数
:<math> f(\eta_i,\eta_j)=\Theta(\eta_i+\eta_j-Z)</math>
:<math> f(\eta_i,\eta_j)=\Theta(\eta_i+\eta_j-Z)</math>
with <math>Z</math> a constant and <math>\Theta</math> the Heavyside function, we also obtain
scale-free networks.
其中 <math>Z</math> 是常数且 <math>\Theta</math> 是 Heavyside函数，我们同样得到了无标度网络。
其中 <math>Z</math> 是常数且 <math>\Theta</math> 是 Heavyside函数，我们同样得到了无标度网络。
Such model has been successfully applied to describe trade between nations by using GDP as fitness for the various nodes <math>i,j</math> and a linking function of the kind
<ref>Garlaschelli D., M I Loffredo Physical Review Letters 93, 188701 (2004)</ref>
<ref>Cimini G., T. Squartini, D. Garlaschelli and A. Gabrielli, Scientific Reports 5, 15758 (2015)</ref>
:<math> \frac{\delta \eta_i\eta_j}{1+ \delta \eta_i\eta_j}.</math>
这样的模型在描述国际贸易上很成功，其中GDP作为不同节点的适应性 <math>i,j</math> ，并且连接函数是如下的形式
这样的模型在描述国际贸易上很成功，其中GDP作为不同节点的适应性 <math>i,j</math> ，并且连接函数是如下的形式